\(\frac{{dQ}}{{dt}} = \frac{{kA\left( {{\theta _1} - \theta } \right)}}{x}\)

\( \Rightarrow {\theta _1} - \theta  = \frac{x}{{kA}}\frac{{dQ}}{{dt}} \Rightarrow \theta  = {\theta _1} - \frac{x}{{kA}}\frac{{dQ}}{{dt}}\)

Where \(\theta _1\) is the temperature of hot and \(\theta \) is temperature at a distance \(x\) from hot end.

The above equation can be graphically represented by option \((a)\).